How does the barber paradox illustrate the self-reference involved in Russell’s paradox?

The barber paradox serves as a popular, intuitive illustration of the logical inconsistency found in Russell’s paradox.

In the barber paradox, a village barber claims to shave all those—and only those—who do not shave themselves. This creates a self-referential dilemma: if the barber does not shave himself, he must shave himself according to his own rule; if he does shave himself, he violates the rule that he only shaves those who do not shave themselves.12

This mirrors the structure of Russell’s paradox, which concerns the set of all sets that are not members of themselves ($R=\{x|x\notin x\}$). The paradox arises when asking if $R$ is a member of itself:
* If $R$ is a member of itself, it must satisfy the condition of not being a member of itself.
* If $R$ is not a member of itself, it satisfies the condition of being a member of itself.3

Both paradoxes demonstrate the dangers of self-reference and unrestricted comprehension, where a definition or rule is applied to a class that includes itself, leading to an unavoidable logical contradiction.32